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Table 10 Longitudinal measurement invariance for STMS models following Geiser et al. (2015)

From: Psychological determinants of test motivation in low-stakes test situations: A longitudinal study of singletrait–multistate models in accounting

Model N Par χ2 df χ2/df CFI TLI RMSEA SRMR LLCorFac TRd* TRd p* ∆CFI* ∆RMSEA*
VALUE
M1: no measurement invariance (mi) 486 56 48.99 34 1.44 0.985 0.971 0.030 0.037 1.467     
M2: trait loading mi 486 50 52.82 40 1.32 0.987 0.979 0.026 0.046 1.424 2.83 0.83 0.002 − 0.004
M3: trait loading and intercept mi 486 44 68.95 46 1.50 0.977 0.968 0.032 0.054 1.422 16.21 0.01 − 0.010 0.006
M4: trait loading. intercept and state loading mi 486 38 80.64 52 1.55 0.972 0.964 0.034 0.058 1.441 11.44 0.08 − 0.005 0.002
EFFOR
M1: no measurement invariance (mi) 486 86 199.83 103 1.94 0.959 0.939 0.044 0.054 1.306     
M2: trait loading mi 486 76 204.80 113 1.81 0.961 0.947 0.041 0.062 1.295 3.64 0.96 0.002 − 0.003
M3: trait loading and intercept mi 486 66 217.29 123 1.77 0.960 0.950 0.040 0.066 1.279 11.52 0.32 − 0.001 − 0.001
M4: trait loading. intercept and state loading mi 486 56 259.26 133 1.95 0.946 0.938 0.044 0.060 1.365 31.31 0.00 − 0.014 0.004
INTRI
M1: no measurement invariance (mi) 612 71 139.92 64 2.19 0.982 0.970 0.044 0.038 1.433     
M2: trait loading mi 612 63 145.37 72 2.02 0.982 0.974 0.041 0.040 1.485 8.07 0.43 0.000 − 0.003
M3: trait loading and intercept mi 612 55 154.88 80 1.94 0.982 0.977 0.039 0.040 1.522 10.71 0.22 0.000 − 0.002
M4: trait loading. intercept and state loading mi 612 47 165.02 88 1.88 0.982 0.978 0.038 0.044 1.561 11.19 0.19 0.000 − 0.001
IDENT
M1: no measurement invariance (mi) 612 56 49.20 34 1.45 0.994 0.988 0.027 0.032 1.316     
M2: trait loading mi 612 50 65.99 40 1.65 0.990 0.983 0.033 0.051 1.310 17.04 0.01 − 0.004 0.006
M3: trait loading and intercept mi 612 44 84.92 46 1.85 0.985 0.978 0.037 0.055 1.372 16.83 0.01 − 0.005 0.004
M4: trait loading. intercept and state loading mi 612 38 95.85 52 1.84 0.983 0.978 0.037 0.060 1.438 10.97 0.09 − 0.002 0.000
INTRO
M1: no measurement invariance (mi) 612 56 154.56 34 4.55 0.901 0.808 0.076 0.072 1.367     
M2: trait loading mi 612 50 161.45 40 4.04 0.900 0.835 0.070 0.074 1.365 6.65 0.35 − 0.001 − 0.006
M3: trait loading and intercept mi 612 44 167.76 46 3.65 0.900 0.857 0.066 0.075 1.394 8.53 0.20 0.000 − 0.004
M4: trait loading. intercept and state loading mi 612 38 157.48 52 3.03 0.913 0.890 0.058 0.075 1.340 − 24.89 1.00 0.013 − 0.008
EXTRI
M1: no measurement invariance (mi) 612 56 142.67 34 4.20 0.882 0.771 0.072 0.061 1.491     
M2: trait loading mi 612 50 124.75 40 3.12 0.908 0.848 0.059 0.069 1.425 − 33.26 1.00 0.026 − 0.013
M3: trait loading and intercept mi 612 44 130.99 46 2.85 0.908 0.867 0.055 0.071 1.471 8.40 0.21 0.000 − 0.004
M4: trait loading. intercept and state loading mi 612 38 132.20 52 2.54 0.913 0.889 0.050 0.071 1.459 0.09 1.00 0.005 − 0.005
ACMOT
M1: no measurement invariance (mi) 779 56 47.52 34 1.40 0.991 0.982 0.023 0.034 1.214     
M2: trait loading mi 779 50 57.90 40 1.45 0.988 0.980 0.024 0.045 1.239 10.18 0.12 − 0.003 0.001
M3: trait loading and intercept mi 779 44 79.40 46 1.73 0.978 0.968 0.031 0.055 1.251 20.70 0.00 − 0.010 0.007
M4: trait loading. intercept and state loading mi 779 38 85.21 52 1.64 0.978 0.972 0.029 0.056 1.259 6.03 0.42 0.000 − 0.002
ASELF
M1: no measurement invariance (mi) 779 95 339.81 157 2.16 0.954 0.938 0.039 0.051 1.236     
M2: trait loading mi 779 89 397.26 163 2.44 0.941 0.924 0.043 0.069 1.270 39.20 0.00 − 0.013 0.004
M3: trait loading and intercept mi 779 77 457.42 175 2.61 0.929 0.914 0.046 0.068 1.303 52.18 0.00 − 0.012 0.003
M4: trait loading. intercept and state loading mi 779 65 454.67 187 2.43 0.932 0.924 0.043 0.067 1.282 − 13.66 1.00 0.003 − 0.003
  1. VALUE, Subjective test value; EFFOR, Effort. INTRI, Intrinsic regulation; IDENT, Identified regulation; INTRO, Introjected regulation; EXTRI, External regulation; ACMOT, Achievement motivation; ASELF, Academic self-concept. N, sample size; Par, number of estimated parameters. χ2, Chi square value; df, degrees of freedom; CFI, Comparative Fit Index; TLI, Tucker Lewis Index; RMSEA, Root Mean Square Error of Approximation; SRMR, Standardized Root Mean Square Residual. LLCorFac, Scaling Correction Factor for MLR; TRd, Satorra-Bentler scaled Chi square difference test
  2. *The current model (M) is compared to the previous model (M-1). Substantial losses in model fit (> − 0.01 CFI, > . 0.15 RMSEA) according to Chen (2007) are given in italics